Skip Navigation

13.1: Inverse Variation

Difficulty Level: At Grade Created by: CK-12
Turn In

This activity is intended to supplement Algebra I, Chapter 12, Lesson 1.

Part 1 - Enter the Data

Enter the data from the table into lists.

Press STAT ENTER. Enter the \begin{align*}x\end{align*}x column in \begin{align*}L1\end{align*}L1 and the \begin{align*}y\end{align*}y column in \begin{align*}L2\end{align*}L2 as shown.

\begin{align*}x\end{align*}x \begin{align*}y\end{align*}y
1 \begin{align*} 24\end{align*}24
2 \begin{align*}12\end{align*}12
3 \begin{align*}8\end{align*}8
4 \begin{align*}6\end{align*}6
5 \begin{align*}4.8\end{align*}4.8
6 \begin{align*}4\end{align*}4

Press \begin{align*}Y=\end{align*}Y=, and select Plot1.

Press ENTER to turn the plot On. Select scatter as the type of plot, \begin{align*}L1\end{align*}L1 for the Xlist, and \begin{align*}L2\end{align*}L2 for the Ylist.

Press WINDOW. Set the window to the following:

\begin{align*}Xmin = 0,\ Xmax = 10,\ Xscl = 2\end{align*}Xmin=0, Xmax=10, Xscl=2

\begin{align*}Ymin = 0,\ Ymax = 25,\ Yscl = 5\end{align*}Ymin=0, Ymax=25, Yscl=5

Press GRAPH.

Part 2 - Questions

  • How would you describe the relationship between \begin{align*}x\end{align*}x and \begin{align*}y\end{align*}y by examining this data?

Press STAT ENTER to return to the lists.

  • What relationships can you see by examining the numbers in the lists?
  • What is the product of each pair of numbers?

Arrow to the top of \begin{align*}L3\end{align*}L3. Enter a formula to multiply the entries in \begin{align*}L1\end{align*}L1 by the entries in \begin{align*}L2\end{align*}L2. Press \begin{align*}2^{nd}\ [L1]\end{align*}2nd [L1] for \begin{align*}L1\end{align*}L1 and press \begin{align*}2^{nd}\ [L2]\end{align*}2nd [L2] for \begin{align*}L2\end{align*}L2. \begin{align*}L3 = L1*L2\end{align*}L3=L1L2

Press ENTER to execute the formula. The product in each case is \begin{align*}24\end{align*}24. So, \begin{align*}L1 \cdot L2 = 24\end{align*}L1L2=24 or \begin{align*}x \cdot y = 24\end{align*}xy=24. This relationship, when \begin{align*}x\end{align*}x and \begin{align*}y\end{align*}y have a constant product, is called “inverse variation.”

  • What type of situation might this be a formula for?

Solve the equation \begin{align*}x \cdot y = 24\end{align*}xy=24 for \begin{align*}y\end{align*}y. Press \begin{align*}Y=\end{align*}Y=. Enter the equation into \begin{align*}Y1\end{align*}Y1.

  • What is your equation?

Press GRAPH.

  • What other information can you find from the graph of the equation that you could not gather from the plot?
  • Does this graph appear to be a function? Explain.

Press \begin{align*}2^{nd}\end{align*}2nd [TABLE] to examine the function table.

  • What is happening when \begin{align*}x = 0\end{align*}x=0? Why?

Arrow up to the negative \begin{align*}x-\end{align*}xvalues in the table.

  • What do you notice about the \begin{align*}y-\end{align*}yvalues?
  • Why does this occur?
  • What do you think the graph of your equation looks like to the left of the \begin{align*}y-\end{align*}yaxis?

Press WINDOW. Set the window as shown to examine the graph when \begin{align*}x\end{align*}x is negative.

Press GRAPH.

  • What appears to be happening when \begin{align*}x = 0\end{align*}x=0?
  • Why does the graph of the equation not appear in Quadrants II or IV?
  • Do you think an inverse variation can ever be found in Quadrants II or IV? Why?
  • Does this graph appear to be a function now? Explain.

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Date Created:
Feb 22, 2012
Last Modified:
Oct 31, 2014
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the section. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original